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If vecA=lamda(vecuxxvecv)+mu(vecvxxvecw)...

If `vecA=lamda(vecuxxvecv)+mu(vecvxxvecw)+nu(vecwxxvecu) and [vecu vecv vecw]=1/5 then lamda +mu+nu=` (A) 5 (B) 10 (C) 15 (D) none of these

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The correct Answer is:
6
q= Area of parallelogram with `vec(OA) and vec(OC)` as adjacent sides
`|vec(OA) xx vec(OC)|`
`|veca xx vecb|`
p = Area of quadrilateral OABC
`1/2|vec(OA)xx vec(OB)|+1/2|vec(OB)xx vec(OC)|`
`1/2[|veca xx(10 veca + 2vecb)|+|(10veca + 2vecb)xxvecb|]`
`1/2|(12veca xx vecb)|=6|veca xx vecb| Rightarrow k =6`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. let veca , vecb and vecc be three vectors having magnitudes 1, 1 and 2...

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  2. A, B C and D are four points in a plane with position vectors, veca, v...

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  3. If vecA=lamda(vecuxxvecv)+mu(vecvxxvecw)+nu(vecwxxvecu) and [vecu vecv...

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  4. If veca = hatj + sqrt3hatk vecb= - hatj + sqrt3 hatk and vecc = 2sqrt3...

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  5. If veca,vecb,vecc be unit vectors such that veca.vecb=veca.vecc=0 and ...

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  6. If vecx.veca=0 , vecx.vecb=0 , vecx.vecc=0 and vecxnevec0 ...

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  7. for any three vectors, veca, vecb and vecc , (veca-vecb) . (vecb -vecc...

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  8. The scalar vecA.(vecB+vecC)xx(vecA+vecB+vecC) equals (A) 0 (B) [vecA v...

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  9. For non zero vectors veca,vecb, vecc |(vecaxxvecb).vecc|=|veca||vecb...

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  10. The volume of he parallelepiped whose sides are given by vec O A=2...

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  11. If veca , vecb , vecc are three non-coplanar vector and vecp...

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  12. Let veca=hati-hatj, vecb=hatj-hatk, vecc=hatk-hati. If hatd is a unit ...

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  13. If veca, vecb, vecc are three non - coplanar vector such that vecaxx(v...

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  14. Let vecu, vecv and vecw be vector such that vecu+vecv+vecw=vec0. If |v...

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  15. If veca, vecb and vecc1 are three non-coplanar vectors, then (veca + v...

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  16. vec p , vec q ,a n d vec r are three mutually perpendicular vectors of...

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  17. Let veca=2vecj+vecj-2veck,vecb=veci+vecj. If vecc is a vector such tha...

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  18. Let vec a=2i+j+k , vec b=i+2j-k and a unit vector vec c be coplanar....

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  19. If the vectors veca,vecb,vecc form the sides BC,CA and AB respectively...

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  20. Consider the vectors, vec(a),vec(b),vec(c),vec(d) such that (vec(a)xxv...

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